How can I separate faces without the edges?
You can get the same functionality with Extrude individual Faces (the easiest way to access this function is by pressing space and just typing it in).

If your Pivot Point is set to Individual Origins and you are in Face select mode, you can then also scale the individual faces down independantly with S.

With Select > Inverse and X > Faces, you can delete everything in-between.

Steps: